Today is 1 July, 2019. Carole has a portfolio which consists of two different types of financial instruments (henceforth referred to as instrument A and instrument B). Carole purchased all instruments on 1 July 2011 to create this portfolio, which is composed of 40 units of instrument A and 21 units of instrument B.

• Instrument A is a zero-coupon bond with a face value of $100. This bond matures at par. Its maturity date is 1 January 2029.
• Instrument B is a Treasury bond with a coupon rate of j₂=4.78% p.a. and a face value of $100. This bond matures at par. Its maturity date is 1 January 2022.

What is the duration of instrument B? Express your answer in terms of years and round your answer to three decimal places. Assume a yield rate of j₂=2.34% p.a.

a.

5.674 years

b.

2.837 years

c.

2.390 years

d.

4.779 years